A Characterization of Families of Graphs in Which Election Is Possible

Extended Abstract
  • Emmanuel Godard
  • Yves Métivier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2303)


The Model. We consider networks of processors with arbitrary topology. A network is represented as a connected, undirected graph where vertices denote processors and edges denote direct communication links. Labels (or states) are attached to vertices and edges. Labels are modified locally, that is, on a subgraph of fixed radius 1 of the given graph, according to certain rules depending on the subgraph only (local computations). The relabelling is performed until no more transformation is possible, i.e., until a normal form is obtained.

The Problem. The election problem is one of the paradigms of the theory of distributed computing. Considering a network of processors the election problem is to arrive at a configuration where exactly one process is in the state elected and all other processes are in the state non-elected see [Tel00]. The elected vertex is used to make decisions, to centralize or to broadcast some information.

Known Results. Graphs where election is possible were already studied but the algorithms usually involved some particular knowledge. Solving the problem for different knowledge has been investigated for some particular cases including (see [Tel00] for details): - the network is known to be a tree - the network is known to be complete - the network is known to be a grid - the nodes have different identification numbers - the network is known to be a ring and has a known prime number of vertices.


  1. Ang80.
    D. Angluin. Local and global properties in networks of processors. In Proceedings of the 12th Symposium on theory of computing, pages 82–93, 1980.Google Scholar
  2. BV99.
    P. Boldi and S. Vigna. Computing anonymously with arbitrary knowledge. In Proceedings of the 18th ACM Symposium on principles of distributed computing, pages 181–188. ACM Press, 1999.Google Scholar
  3. FHR72.
    J.-R. Fiksel, A. Holliger, and P. Rosenstiehl. Intelligent graphs. In R. Read, editor, Graph theory and computing, pages 219–265. Academic Press (New York), 1972.Google Scholar
  4. Godar.
    E. Godard. A self-stabilizing enumeration algorithm. Inform. Proc. Letters, to appear.Google Scholar
  5. KY96.
    T. Kameda and M. Yamashita. Computing on anonymous networks: Part i-characterizing the solvable cases. IEEE Transactions on parallel and distributed systems, 7(1):69–89, 1996.CrossRefGoogle Scholar
  6. Mas91.
    W. S. Massey. A basic course in algebraic topology. Springer-Verlag, 1991 Graduate texts in mathematics.Google Scholar
  7. Maz97.
    A. Mazurkiewicz. Distributed enumeration. Inf. Processing Letters, 61:233–239, 1997.CrossRefMathSciNetGoogle Scholar
  8. MMW97.
    Y. Métivier, A. Muscholl, and P.-A. Wacrenier. About the local detection of termination of local computations in graphs. In International Colloquium on structural information and communication complexity, pages 188–200, 1997.Google Scholar
  9. MT00.
    Y. Métivier and G. Tel. Termination detection and universal graph reconstruction. In International Colloquium on structural information and communication complexity, pages 237–251, 2000.Google Scholar
  10. SSP85.
    B. Szymanski, Y. Shy, and N. Prywes. Terminating iterative solutions of simultaneous equations in distributed message passing systems. In Proceedings of the 4th Symposium on Principles of Distributed computing, pages 287–292, 1985.Google Scholar
  11. Tel00.
    G. Tel. Introduction to distributed algorithms. Cambridge University Press, 2000.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Emmanuel Godard
    • 1
  • Yves Métivier
    • 1
  1. 1.LaBRIUniversité Bordeaux I, ENSEIRBTalenceFrance

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